Thinking about something.
What happens when you tune a box below the resonant frequency by a driver?
The same for above the resonant frequency by a driver?
Is it only the base that is affected?
Thinking of a box that has a base tube.
You can calculate the length using the resonance frequency as a starting point.
If you make the bass tube longer or shorter, the tuning is lower or higher, respectively.
How will the sound be affected if the tube gets shorter and longer?
What happens when you tune a box below the resonant frequency by a driver?
The same for above the resonant frequency by a driver?
Is it only the base that is affected?
Thinking of a box that has a base tube.
You can calculate the length using the resonance frequency as a starting point.
If you make the bass tube longer or shorter, the tuning is lower or higher, respectively.
How will the sound be affected if the tube gets shorter and longer?
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You extend the low-frequency response if the Q factor is high enough. You end up with a Chebyshev alignment then, or something close to it.
This is Thiele's famous table of loudspeaker alignments with reasonably flat responses. f3/fb is the ratio of the -3 dB frequency to the box tuning frequency and f3/fs the ratio of the -3 dB frequency to the resonant frequency of the driver. The ratio (f3/fs)/(f3/fb) = fb/fs is the ratio of the box tuning frequency to the resonant frequency of the driver.
Thiele also found a way to interpolate between the alignments (see the last two columns). The fifth- and sixth-order alignments require a first- or second-order electrical high-pass filter somewhere in the signal path.
This is Thiele's famous table of loudspeaker alignments with reasonably flat responses. f3/fb is the ratio of the -3 dB frequency to the box tuning frequency and f3/fs the ratio of the -3 dB frequency to the resonant frequency of the driver. The ratio (f3/fs)/(f3/fb) = fb/fs is the ratio of the box tuning frequency to the resonant frequency of the driver.
Thiele also found a way to interpolate between the alignments (see the last two columns). The fifth- and sixth-order alignments require a first- or second-order electrical high-pass filter somewhere in the signal path.
The effect of any port extends beyond the region we are designing it for because of pipe resonances in the port itself, which can extend well into the midrange.
The length of the port simply determines where these resonances will occur.
Please find your point of preference with adjustable duct.
I think, verification is more important than theory.
I think, verification is more important than theory.
But the 'theory' is Helmholtz resonance, and the basic physics for that was known to the Ancient Greeks and other societies, & fully established by Helmholtz in 1862. 
Electrical filter theory used in typical vented alignments today is heavily based on Butterworth's work, & goes back to the mid '30s. As far as that goes it's closed-form solved. There are variations from external factors, many of which are also identifiable and easily predictable in advance if you use a comprehensive enough data set, but the theory itself has been verified for 'a while'. Not saying it isn't important to adjust based on other factors like room modes, personal preference etc., obviously, which is where the empirical testing really starts to be valuable.
Electrical filter theory used in typical vented alignments today is heavily based on Butterworth's work, & goes back to the mid '30s. As far as that goes it's closed-form solved. There are variations from external factors, many of which are also identifiable and easily predictable in advance if you use a comprehensive enough data set, but the theory itself has been verified for 'a while'. Not saying it isn't important to adjust based on other factors like room modes, personal preference etc., obviously, which is where the empirical testing really starts to be valuable.
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If we're talking regular ducted vent 'bass reflex' (not really, but we'll go with it) enclosures, then yes & no, as shown above.
As GM says, technically T/S parameters peter out above the mass corner frequency Fhm (take as 2Fs/Qts' where Qts' = Qts + any relevant series R in circuit), with the nominal exception of Le & its variations, which are technically fundamental parameters that got lumped in with what we call T/S values. LF loads are only useful up to that point, & if Fhm is > about 250Hz-300Hz, not even then or group delay will be an issue, apart from rare cases of extreme personal preference. In most cases, because the box / duct naturally forms an LP filter, it will be rolling off well below that point. However, a duct is also a 1/2 wave resonator since it's a pipe of some description or other that's open at both ends, so it will have its own resonant modes (also shown above) that ignoring the effect of end-correction, flares etc. will have a fundamental at lambda/2 & decaying odd & even multiples above that.
To be honest, as you'd expect from the alignment change, which will vary depending on what you started out with. Very broadly, the lower you tune, the more heavily damped it will be & may (may) end up sounding 'tighter' (I hate these subjective terms); as you go the other way & progressively underdamp, so you have a peaking response at & above Fb you'll usually get what you'd expect -a more or less obvious emphasis at that region & potentially greater ringing in the time domain. But this is over-generalised as these things can be manipulated in specific circumstances & for particular purposes, so it's not entirely black / white although as a loose guide it serves.
as MrKlinky pointed out there can be consequences at midrange frequencies but that's where port placement or whether or not your midrange driver is open backed or enclosed and where x-over frequencies lay come to bare.
a two way bass reflex where the bass driver is operated well into upper mid frequencies can have it's performance suffer especially when a single large port with minimal duct is used.
.......also, low Qt drivers in general can have an Fhm well into the mids if not XO'd to limit it......
Don't you just miss the days when we had some relatively well-damped units with a low Fs? 😉 They seem to have gone out of the window since the heyday of Altec, Goodmans (and some of the top '70s JBL gear to be fair to them).
I found this on FB by Bruce David Campell:
When companies are competing with each other with respect to speaker performance at a given price point it is inevitable that they will turn to ported speakers.
A sealed cabinet is easy to design and performs well. The base rolls off at 12 decibels per octave below the resonant frequency and phase response is very good. The Q of the driver needs to be considerably higher than a driver used for a ported design so that the bass can be heard and is pleasing as it centers around the resonant frequency and it requires a smaller enclosure as well.
However as audio engineering became more advanced and refined Engineers soon discovered that they could create better performance for the same price point by using a ported enclosure. This is because they can design for two resonant frequencies one for the Box and then a second one created by the port using the hemholtz affect. In addition something interesting happens and that's that the Excursion of the woofer actually is significantly reduced at the port resonant frequency and this improves power handling immensely you can actually observe this with your eye if you use a signal generator and a high power amplifier whereas a sealed speaker you will see the cone is at maximum Excursion when at resonance. Ported enclosures are much more difficult to design and the roll off below resonance is 24 decibels per octave so sometimes they don't sound as bassy even though their bass is better on a spec sheet but when they're well designed they are the superior speaker without question. The Thiel Small parameters necessary for the woofers are very different and they are not interchangeable.
I really like the sound of sealed enclosures but unfortunately there are very few woofers available nowadays that have the correct parameters to work in an acoustic suspension design .
So sealed enclosures are easier to design but ported enclosures can perform better for the same amount of resources and ultimately they can also be made considerably more efficient.
When companies are competing with each other with respect to speaker performance at a given price point it is inevitable that they will turn to ported speakers.
A sealed cabinet is easy to design and performs well. The base rolls off at 12 decibels per octave below the resonant frequency and phase response is very good. The Q of the driver needs to be considerably higher than a driver used for a ported design so that the bass can be heard and is pleasing as it centers around the resonant frequency and it requires a smaller enclosure as well.
However as audio engineering became more advanced and refined Engineers soon discovered that they could create better performance for the same price point by using a ported enclosure. This is because they can design for two resonant frequencies one for the Box and then a second one created by the port using the hemholtz affect. In addition something interesting happens and that's that the Excursion of the woofer actually is significantly reduced at the port resonant frequency and this improves power handling immensely you can actually observe this with your eye if you use a signal generator and a high power amplifier whereas a sealed speaker you will see the cone is at maximum Excursion when at resonance. Ported enclosures are much more difficult to design and the roll off below resonance is 24 decibels per octave so sometimes they don't sound as bassy even though their bass is better on a spec sheet but when they're well designed they are the superior speaker without question. The Thiel Small parameters necessary for the woofers are very different and they are not interchangeable.
I really like the sound of sealed enclosures but unfortunately there are very few woofers available nowadays that have the correct parameters to work in an acoustic suspension design .
So sealed enclosures are easier to design but ported enclosures can perform better for the same amount of resources and ultimately they can also be made considerably more efficient.
Yeah, you want mine you'll have to pry them from my cold dead hands. That said, from a technical POV unless tube driven and/or horn loaded there's no real need for them nowadays.
Maybe -although I'd just call them on principle a more acoustically efficient approach, and given the choice I'd pick that direction over shed-loads of power and EQ. Sad thing is, there isn't really the option any more. Oh well -maybe that makes us brontosauruses, but I can live with that. 🦕
'Preaching to the choir'! 
, but it's a mighty small one nowadays.
, but it's a mighty small one nowadays.
'Perform better...' in terms of sheer output, absolutely. Perform better in terms of sound quality, definitely not.
When so much about DIY speakers is geared towards reducing enclosure resonances, to deliberately turn the whole thing into a poorly damped resonator can never be a good thing if temporal accuracy of reproduction is of primary interest.
Of course we get more bang-for-our-buck with ported enclosures, but given the huge power handling of modern LF drivers, affordable EQ, and cheap amplifier Watts, if we're not trying to fill a school hall with loud bass, sealed enclosures just have so much going for them.
Personally I'm highly allergic to BR's droning accompaniment. Rather than learning to "critically" dampen the ports I've always stuffed them closed (in disgust; not-inexpensive commercial speakers). On the other hand, my diy folded tapered-TL are clearer, deeper, more dynamic, and MUCH SMALLER. I like sealed and usually test-run a driver that way, but to get 40s bass the cabs are too large for a small apartment in a large city, weigh too much for my bad back, cost too much in materials, and require too much workmanship to make them non-resonant.
If @MrKlinky (or anyone) can do ~1cuft sealed with decent 40s bass (even 50s if smaller), please teach me how.
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"This is because they can design for two resonant frequencies one for the Box and then a second one created by the port using the hemholtz affect."
Is there a formula for this?
How to calculate the different resonance frequencies so that they fit together?
Is there a formula for this?
How to calculate the different resonance frequencies so that they fit together?
If only! My 18" subs are 50l, and the 21" subs are 130l - they have one amplifier each (10 amplifiers) totalling about 20kW continuous behind them. And tons of EQ!
I've just bought a tiny REL 12" powered sub, and whilst impressive for its size, is just trying too hard. With proper EQ it should be quite listenable at lower levels in my workshop system. (4 x Tannoy coaxials).
Well that's not too bad size-wise. What driver and how low sealed? I've tried two 15" isobaric clamshell but 50L too small?
I'm sorry -what's some of this twaddle?
Noting the text is from elsewhere & was simply cited so the quotes are taken in that context:
'An object of this invention is to increase the response of sound translating devices at the lower frequencies whereby the low notes of speach and music are more faithfully translated and in a more proportionate degree to the higher notes than has been possible hitherto'
Thuras, Albert L. 1932.
Note the date and what was physically / practically possible in the majority of circumstances & using the technology of the time in a home audio [such as they were] system.
Noting the text is from elsewhere & was simply cited so the quotes are taken in that context:
It's easy to design (generally) but 'performs well' depends on the design goals; the Q does not necessarily 'need' to be 'considerably higher than a driver used for a ported design'; they don't automatically 'require a smaller enclosure' and I've no idea what 'pleasing' is supposed to mean.
Wrong. Thuras patented a method (which is strictly speaking what a 'bass reflex' is) which he described thus:
'An object of this invention is to increase the response of sound translating devices at the lower frequencies whereby the low notes of speach and music are more faithfully translated and in a more proportionate degree to the higher notes than has been possible hitherto'
Thuras, Albert L. 1932.
Note the date and what was physically / practically possible in the majority of circumstances & using the technology of the time in a home audio [such as they were] system.
Mmm. Not the happiest phrasing. Vented boxes are phase inverters; the air in the box in effect acts as a spring coupling the driver to the air mass trapped in the port [ducted or otherwise]. You don't typically design a Helmholtz based box for 'two [different] resonant frequencies, unless it happens to be a DCR with interconected chambers independently vented to the outside room. The system resonance lies at the impedance minimum.
It improves power handling at system resonance, but because below this point the driver is more or less progressively unbaffled, it will eventually unload at 24dB/octave, significantly reducing power handling if presented with signals below Fb. The maximum driver excursion in a sealed box is not typically 'at resonance' either.
They're different, with a different balance of compromises, that's all. Assuming good design practice, you select a load (whatever type & whatever alignment within that) that suits your needs.
Rubbish. There is often some crossover as-is, and in many cases you can adapt to requirements as part of the design process. Whether you'd want to look at alternate drive units as well is another matter, but that doesn't change the fact of it.
An acoustic suspension enclosure is a specific type of sealed box; it's not the only alignment. It's true that there are far fewer drivers suited to these loads today, mainly because a majority of buyers want 'acoustically small' enclosures for reasons other than acoustic [space, decor, personal preference etc.] but they're far from unknown. You just have to look a bit harder, or make a few [reversible] modifications to other likely candidates.
'Can'. They have the potential for greater efficiency in their limited passband -the overall system efficiency however doesn't change, notwithstanding a few equalisation trends where you may manipulate the response in a narrow band for other purposes -the LS3/5a is a good example of this in a sealed enclosure.